document.write( "Question 241146: I have a question about the powers of \"i\". I am not understanding the facts about how \"i\" to the second power = blank or \"i\" to the 6th powers = blank and so fourth. Can you explain this procedure in detail and explain how it is used in the radical equation?
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #176596 by vleith(2983)\"\" \"About 
You can put this solution on YOUR website!
i is defined as the \"sqrt%28-1%29\"
\n" ); document.write( "So
\n" ); document.write( "i^1 = i
\n" ); document.write( "i^2 = -1
\n" ); document.write( "i^3 = -i
\n" ); document.write( "i^4 = (-1)(-1) = 1
\n" ); document.write( "And it repeats in a cycle of 4
\n" ); document.write( "i^5 = i^4*i = 1+i = i
\n" ); document.write( "i^6 = i^4*i^2 = 1*i^2 = 1 *(-1) = -1
\n" ); document.write( "i^7 = i^4*i^3 = 1*i^3 = -i
\n" ); document.write( "etc etc\r
\n" ); document.write( "\n" ); document.write( "how do you use in a radical? If the value under the radical is negative, then look at that as (-1)*aPositive
\n" ); document.write( "for instance \"sqrt%28-9%29+=+sqrt%28%28-1%29%2A9%29+=+sqrt%28-1%29%2Asqrt%289%29\" = plus or minus 3i
\n" ); document.write( " \n" ); document.write( "
\n" );